Wave Optics PYQs Set 6 (PDF)

Set 6 of 10 · Questions 151-180 of 295

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Optics · Set 6 (Q151-180)
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151. $In a Fraunhofer diffaction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of 30^{\circ} . The direction θ of the first secondary maximum is given by$ (1) $sin^{- 1} (1/4)$ (2) $tan^{- 1} (2/3)$ (3) $sin^{- 1} (2/3)$ (4) $sin^{- 1} (3/4)$ 152. $Light consisting of a plane waves of wavelength, λ_{1} = 8 \times 10^{- 5} cm and λ_{2} = 6 \times 10^{- 5} cm generates an interference pattern in Young's double slit experiment. If n_{1} denotes the n_{1} th dark fringe due to light of wavelength λ_{1} which coincides with n_{2} th bright fringe due to light of wavelength λ_{2}, then$ (1) $n_{1} = 3, n_{2} = 1$ (2) $n_{1} = 4, n_{2} = 5$ (3) $n_{1} = 1, n_{2} = 2$ (4) $n_{1} = 3, n_{2} = 2$ 153. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. choose the correct answer from the options given below :$ (1) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ (2) $(A) is true but (R) is false$ (3) $Both (A) and (R) are true and (R) is the correctexplanation of (A)$ (4) $(A) is false but (R) is true$ 154. $The sources of light of wavelength 2500Å and 3500 A are used in Youngs double slit experiment simultaneously: Which orders of fringes of two wavelength patterns coincide?$ (1) $3^{nd} order of 1^{st} and 5^{th} order of 2^{nd}$ (2) $7^{th} order of 1^{st} and 5^{th} order of 2^{nd}$ (3) $5^{th} order of 1^{st} and 3^{rd} order of 2^{nd}$ (4) $5^{th} order of 1^{st} and 7^{th} order of 2^{nd}$ 155. $In Fraunhofer diffraction pattern, slit width is and screen is at away from the lens. If wavelength of light used is then the distance between the first minimum on either side the central maximum is ( is small and measured in radian)$ (1) $10^{- 1} m$ (2) $10^{- 2} m$ (3) $2\times 1 0^{- 2} m$ (4) $2\times 1 0^{- 1} m$ 156. $In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case:$ (1) $there shall be alternate interference fringes of red and green.$ (2) $there shall be an interference pattern for red distinct from that for green. there shall be an interference pattern,$ (3) $where each fringe's pattern center is green and outer edges is red.$ (4) $there shall be no interference fringes.$ 157. $Two plane polarized light waves combine at a certain point whose electric field components are E_{1} = E_{0} Sinωt E_{2} = E_{0} Sin (ωt + \frac{π}{3}) Find the amplitude of the resultant wave.$ (1) $1.7 E_{0}$ (2) $E_{0}$ (3) $0.9 E_{0}$ (4) $3.4 E_{0}$ 158. $Two slits separated by 0.5 mm are illuminated by light of wavelength 500 nm . The screen is at a distance of 120 cm from the slits. The phase difference between the interfering waves at a point 3 mm on the screen from the central bright fringe is\dots\dots\dots\dots.$ (1) $5 π$ (2) $π$ (3) $3 π$ (4) $7 π$ 159. $The diffraction pattern of a light of wavelength diffracting from a slit of width is focused on the focal plane of a convex lens of focal length . The width of the secondary maxima will be :$ (1) $2 mm$ (2) $2 cm$ (3) $0.02 mm$ (4) $0.2 mm$ 160. $In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is :$ (1) $15.6 mm$ (2) $1.56 mm$ (3) $7.8 mm$ (4) $9.75 mm$ 161. $To observe diffraction, the size of the obstacle$ (1) $should be λ /2, where λ is the wavelength$ (2) $should be of the order of wavelength$ (3) $has no relation to wavelength$ (4) $should be much larger than the wavelength.$ 162. $Light of wavelength is incident on a single slit of width and the distance between slit and screen is . In diffraction pattern, if slit width is equal to the width of the central maximum, then is equal to$ (1) $a /2 λ$ (2) $a^{2} /2 λ$ (3) $a / λ$ (4) $a^{2} / λ$ 163. $When the angle of incidence is 60^{\circ} on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is$ (1) $2 \times 10^{8} ms^{- 1}$ (2) $3 \times 10^{8} ms^{- 1}$ (3) $2 \times 10^{8} m s^{- 1}$ (4) $3 \times 10^{8} m s^{- 1}$ 164. $Diameter of the objective lens of a telescope is 250 cm . For light of wavelength 600 nm . Coming from a distant object, the limit of resolution of the telescope is close to:$ (1) $1.5 \times 10^{- 7} rad$ (2) $2.0 \times 10^{- 7} rad$ (3) $3.0 \times 10^{- 7} rad$ (4) $4.5 \times 10^{- 7} rad$ 165. $Two coherent plane waves of identical frequency and intensity (I) interfere at a point, where they differ in phase by 60^{\circ} . What is the resulting intensity?$ (1) $I$ (2) $2 I$ (3) $3 I$ (4) $41$ 166. $Two coherent monochromatic light beams of intensities ' 4 r and ' 9 r are superimposed. The maximum and minimum possible intensities in the resulting beam are$ (1) $3I and 2 I$ (2) $9 I and 5 I$ (3) $16 I and 3I$ (4) $25 I and I$ 167. $Visible light of wavelength falls normally on single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at from the central maximum. If the first minimum is produced at , then is close to :$ (1) $25^{\circ}$ (2) $30^{\circ}$ (3) $20^{\circ}$ (4) $45^{\circ}$ 168. $A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just 10 % of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is:$ (1) $45^{\circ}$ (2) $90^{\circ}$ (3) $71.6^{\circ}$ (4) $18.4^{\circ}$ 169. $Light of wavelength ' ' is incident on a slit of width ' ' 'The resulting diffraction pattern is observed on a screen at a distance ' '. The linear width of the principal maximum is then equal to the width of the slit if equals$ (1) $\frac{d}{λ}$ (2) $\frac{d ^{2}}{2 λ}$ (3) $\frac{2 λ}{d}$ (4) $\frac{2 λ ^{2}}{d}$ 170. $In a Young's double slit experiment, m^{th} order and n^{th} order of bright fringes are formed at point P on a distant screen, if monochromatic source of wavelength 400 nm and 600 nm are used respectively. The minimum value of m and n are respectively$ (1) $4,6$ (2) $3,2$ (3) $2,3$ (4) $4,2$ 171. $When a Compact Disc (CD) is illuminated by small source of white light, coloured bands are observed. This is due to$ (1) $interference$ (2) $scattering$ (3) $reflection$ (4) $diffraction.$ 172. $The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:$ (1) $1 : 1$ (2) $4 : 1$ (3) $9 : 1$ (4) $16 : 1$ 173. $In Young's double slit experiment, fringes of width β are produced on a screen kept at a distance of 1 m from the slit. When the screen is moved away by 5 \times 10^{- 2} m, fringe width changes by 3 \times 10^{- 5} m . The separation between the slits is 1 \times 10^{- 3} m . The wavelength of the light used is nm .$ (1) $500$ (2) $600$ (3) $700$ (4) $400$ 174. $White light reflected from a soap film (Refractive index ) has a maxima at and a minima at with no minimum in between. Then the thickness of the film is .$ (1) $1$ (2) $2$ (3) $3$ (4) $4$ 175. $In biprism experiment, the distance between source and eyepiece is 1.2 m, the distance between two virtual sources is 0.84 mm . Then the wavelength of light used if eyepiece is to be moved transversely through a distance of 2.799 cm to shift 30 fringes is$ (1) $6533Å$ (2) $6531Å$ (3) $6535Å$ (4) $6351Å$ 176. $An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30^{\circ} in clockwise direction, the intensity of emerging light will be___Lumens.$ 177. $A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is____\times 10^{- 5} m .$ 178. $A parallel beam of monochromatic light of wavelength is incident normally on a single narrow slit of width . The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of _______(degree).$ 179. $In a Young's double slit experiment, the slits are separated by 0.3mm and the screen is 1.5m away from the plane of slits. Distance between fourth bright fringes on both sides of central bright is 2.4cm. The frequency of light used is .... x 1 0^{14} Hz$ 180. $In a Young's double slit experiment, the intensity at a point is (\frac{1}{4})^{th} of the maximum intensity, the minimum distance of the point from the central maximum is_____μ m . (Given : λ = 600 nm, d = 1.0 mm, D = 1.0 m)$